 
(* ::Section:: *)
(* Nielsen *)
(* ::Text:: *)
(*Nielsen[i, j, x] denotes Nielsen's polylogarithm..*)


(* ::Subsection:: *)
(* See also *)
(* ::Text:: *)
(*SimplifyPolyLog.*)



(* ::Subsection:: *)
(* Examples *)



Nielsen[1,2,x]


(* ::Text:: *)
(*Numerical evaluation is done via N[Nielsen[n_,p_,x_]] := (-1)^(n+p-1)/(n-1)!/p! NIntegrate[Log[1-x t]^p Log[t]^(n-1)/t,{t,0,1}];*)


N[Nielsen[1,2,.45]]


(* ::Text:: *)
(*Some special values are built in.*)


{Nielsen[1,2,0],Nielsen[1,2,-1],Nielsen[1,2,1/2],Nielsen[1,2,1]}

Nielsen[1,2,x,PolyLog->True]

Nielsen[1,3,x,PolyLog->True]

Nielsen[3,1,x,PolyLog->True]
